1. Field
The present invention relates generally to a method of determining inventory levels, and more particularly, to a method of determining inventory reorder levels and order-up-to levels.
2. Description of the Related Art
In inventory management, some items are demanded more frequently and some less frequently. For example, certain repair parts that apply to complex systems and are infrequently demanded must still be stocked because they are essential to maintaining that system. Due to the sporadic demand, however, it is difficult to decide when to order the infrequently demanded items and in what quantities.
For frequently demanded items, there is a well-developed theory and set of processes for ordering that balances the investment in inventory with customer service. However, for items that are infrequently demanded, the theory used for ordering frequently demanded items breaks down and is not effective.
An inventory management system for a single site typically manages each item using two control levels: an item's reorder point (ROP), which determines when to order the item, and a requisitioning objective (RO), which determines how much of the item to order. An order is placed when assets on-hand plus on-order decrease to or below the ROP, and the difference between the RO and the current assets is the quantity ordered. The RO is usually the ROP plus a nominal order quantity, Q, which is often a Wilson Lot-size formula (EOQ) (“economic order quantity”). Thus Q is the quantity ordered if assets drop exactly to the ROP. The ROP is an estimate of lead-time demand (LTD) plus a safety level that protects against variability in LTD.
Safety-level computations usually treat the number of demands in a lead-time as a random variable with a tractable theoretical probability distribution (e.g., Poisson, negative binomial, Laplace, or normal), estimate the mean and variance, and derive expressions for expected backorders and inventory cost as a function of the safety level. Mathematical optimization techniques are then used to set item safety levels to balance inventory investment with expected backorders, probability of a stockout, or system availability. This approach to optimizing ordering policies has been developed and extended to optimize policies across a supply chain, account for repair actions as well as ordering actions, and treat items that apply to diverse, complex systems with distinct availability goals. When there is sufficient demand data to characterize the lead-time demand distribution, but theoretical distributions do not fit well, non-parametric techniques, such as the bootstrap method, may apply.
However, for sporadic-demand items—items that experience long and irregular periods of inactivity between demands (i.e., periods of inactivity from six months to several years)—lead-time demand is usually zero. Forecasting lead-time demand and demand variance for these items is difficult. As mean and variance cannot be estimated in a meaningful way, a theoretical demand probability distribution is impractical. Use of empirical demand probabilities is possible, but for many sporadic-demand items, the data are too sparse to build a reasonable lead-time demand distribution. For example, if an item's only observed demands in the last five years comprise a demand for 8 units and another demand for 50 units, there is no reason to believe a demand for 20 units has a probability of zero.
Inventory management specialists have sought a successful approach to setting ROPs and ROs for sporadic-demand items using heuristic methods. However, the policies used fail to link inventory investment to service level, and generally do not work well. More sophisticated approaches include approaches taken by Croston and Kruse.
Croston shows that, when there is a constant probability of demand in a time interval, high fill rates can be obtained by basing ROPs on separate forecasts of both the time of next demand and demand size (Croston, J. D., “Forecasting Stock Control for Intermittent Demands”). Kruse divides an item's population into subsets by pooling items with similar lead-times, prices, and demand frequencies to thereby obtain enough demand data for empirical lead-time demand probabilities. Kruse assigns each item subset a common ROP based on a fill rate goal. However, for very irregular demand, these approaches have not been shown to improve service levels (e.g., reduce customer wait-time) without significantly increasing inventory investment.
Typically, inventory management systems that distinguish between items with more regular demand and those with sporadic demand use a three-part policy. One part is an ordering policy for frequently-demanded items with ROPs and ROs based on statistical forecasts. The second part is an activity threshold, generally set in terms of historical requisition frequency and quantity, which separates frequently-demanded items from sporadic-demand items. Part three is a heuristic ordering policy employed for items with activity levels below the activity threshold.
In an example of a three-part ordering policy in an inventory management system, frequent-demand items are separated from sporadic-demand items with an activity threshold that is based on the previous year's demand. For items with demand activity below the activity threshold, the inventory management system uses a heuristic policy that sets the RO to the demand quantity in the preceding year and the ROP to half the RO. A problem inherent in this approach is that the heuristic policy does not link inventory cost to service level. Further, items may migrate over the course of the year between frequent-demand and sporadic-demand status, causing excessive ordering and changes in ROs.